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%I #7 Sep 02 2018 14:46:11
%S 428,542,668,806,956,1118,1292,1478,1676,1886,2108,2342,2588,2846,
%T 3116,3398,3692,3998,4316,4646,4988,5342,5708,6086,6476,6878,7292,
%U 7718,8156,8606,9068,9542,10028,10526,11036,11558,12092,12638,13196,13766,14348
%N Number of 6 X 6 0..n matrices with each 2 X 2 subblock idempotent.
%H R. H. Hardin, <a href="/A224668/b224668.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*n^2 + 96*n + 326.
%F Conjectures from _Colin Barker_, Sep 02 2018: (Start)
%F G.f.: 2*x*(214 - 371*x + 163*x^2) / (1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
%F (End)
%e Some solutions for n=3:
%e ..1..0..0..0..1..0....1..1..1..1..1..0....1..0..1..0..0..3....1..0..1..0..0..1
%e ..1..0..0..0..1..0....0..0..0..0..0..0....1..0..1..0..0..1....1..0..1..0..0..1
%e ..1..0..0..0..1..0....1..1..1..1..1..1....0..0..1..0..0..1....1..0..1..0..0..1
%e ..1..0..0..0..1..0....0..0..0..0..0..0....0..0..1..0..0..1....1..0..1..0..0..1
%e ..1..0..0..0..1..0....1..1..1..1..1..1....0..0..1..0..0..1....1..0..1..0..0..1
%e ..2..0..0..0..1..0....0..0..0..0..0..0....0..0..1..0..0..1....0..0..1..0..0..1
%Y Row 6 of A224665.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 14 2013
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